Puiseux series

A formal series of the form

$$\sum _{n=m}^{\mathrm{\infty }}{a}_n{z}^{n/k}$$

where $m$ and $k$ are integers such that $k\ge 1$ isis called a Puiseux series or a fractional power series. Note that if $k>1$, then $z^{n/k}$ could be multivalued. One example of the use of such a power series is the Puiseux parametrization of one-dimensional complex analytic varieties.